Ordinal data: Data in which an ordering or
ranking of responses is possible but no measure of distance is
possible.

Interval data: Generally integer data in
which ordering and distance measurement are possible.

Ratio data: Data in which meaningful
ordering, distance, decimals and fractions between variables
are possible.

Data analyses using nominal, interval and ratio data are
generally straightforward and transparent. Analyses of ordinal
data, particularly as it relates to Likert or other scales in
surveys, are not. This is not a new issue. The adequacy of
treating ordinal data as interval data continues to be
controversial in survey analyses in a variety of applied
fields.1,2

An underlying reason for analyzing ordinal data as interval
data might be the contention that parametric statistical tests
(based on the central limit theorem) are more powerful than
nonparametric alternatives. Also, conclusions and interpretations
of parametric tests might be considered easier to interpret and
provide more information than nonparametric alternatives.

However, treating ordinal data as interval (or even ratio)
data without examining the values of the dataset and the
objectives of the analysis can both mislead and misrepresent the
findings of a survey. To examine the appropriate analyses of
scalar data and when its preferable to treat ordinal data as
interval data, we will concentrate on Likert scales.

Basics of Likert Scales

Likert scales were developed in 1932 as the familiar
five-point bipolar response that most people are familiar with
today.3 These scales range from a group of
categories—least to most—asking people to indicate
how much they agree or disagree, approve or disapprove, or
believe to be true or false. There’s really no wrong way to
build a Likert scale. The most important consideration is to
include at least five response categories. Some examples of
category groups appear in Table 1.

The ends of the scale often are increased to create a
seven-point scale by adding “very” to the respective
top and bottom of the five-point scales. The seven-point scale
has been shown to reach the upper limits of the scale’s
reliability.4 As a general rule, Likert and others
recommend that it is best to use as wide a scale as possible. You
can always collapse the responses into condensed categories, if
appropriate, for analysis.

With that in mind, scales are sometimes truncated to an even
number of categories (typically four) to eliminate the
“neutral” option in a “forced choice”
survey scale. Rensis Likert’s original paper clearly
identifies there might be an underlying continuous variable whose
value characterizes the respondents’ opinions or attitudes
and this underlying variable is interval level, at
best.5

Analysis, Generalization To Continuous Indexes

As a general rule, mean and standard deviation are invalid
parameters for descriptive statistics whenever data are on
ordinal scales, as are any parametric analyses based on the
normal distribution. Nonparametric procedures—based on the
rank, median or range—are appropriate for analyzing these
data, as are distribution free methods such as tabulations,
frequencies, contingency tables and chi-squared statistics.

Kruskall-Wallis models can provide the same type of results as
an analysis of variance, but based on the ranks and not the means
of the responses. Given these scales are representative of an
underlying continuous measure, one recommendation is to analyze
them as interval data as a pilot prior to gathering the
continuous measure.

Table 2 includes an example of misleading conclusions, showing
the results from the annual Alfred P. Sloan Foundation survey of
the quality and extent of online learning in the United States.
Respondents used a Likert scale to evaluate the quality of online
learning compared to face-to-face learning.

While 60%-plus of the respondents perceived online learning as
equal to or better than face-to-face, there is a persistent
minority that perceived online learning as at least somewhat
inferior. If these data were analyzed using means, with a scale
from 1 to 5 from inferior to superior, this separation would be
lost, giving means of 2.7, 2.6 and 2.7 for these three years,
respectively. This would indicate a slightly lower than average
agreement rather than the actual distribution of the
responses.

A more extreme example would be to place all the respondents
at the extremes of the scale, yielding a mean of
“same” but a completely different interpretation from
the ac-tual responses.

Under what circumstances might Likert scales be used with
interval procedures? Suppose the rank data included a survey of
income measuring $0, $25,000, $50,000, $75,000 or $100,000
exactly, and these were measured as “low,”
“medium” and “high.”

The “intervalness” here is an attribute of the
data, not of the labels. Also, the scale item should be at least
five and preferably seven categories.

Another example of analyzing Likert scales as interval values
is when the sets of Likert items can be combined to form indexes.
However, there is a strong caveat to this approach: Most
researchers insist such combinations of scales pass the
Cronbach’s alpha or the Kappa test of intercorrelation and
validity.

Also, the combination of scales to form an
interval level index assumes this combination forms an underlying
characteristic or variable.

Alternative Continuous Measures for Scales

Alternatives to using a formal Likert scale can be the use of
a continuous line or track bar. For pain measurement, a 100 mm
line can be used on a paper survey to measure from worst ever to
best ever, yielding a continuous interval measure.

In the advent of many online surveys, this can be done with
track bars similar to those illustrated in Figure 1. The
respondents here can calibrate their responses to continuous
intervals that can be captured by survey software as continuous
values.

Conclusion

Your initial analysis of Likert scalar data should not involve
parametric statistics but should rely on the ordinal nature of
the data. While Likert scale variables usually represent an
underlying continuous measure, analysis of individual items
should use parametric procedures only as a pilot analysis.

Combining Likert scales into indexes adds values and
variability to the data. If the assumptions of normality are met,
analysis with parametric procedure can be followed. Finally,
converting a five or seven category instrument to a continuous
variable is possible with a calibrated line or track bar.

I. ELAINE ALLEN is an associate professor of
statistics and entrepreneurship at Babson College in Babson Park,
MA. She has a doctorate in statistics from Cornell University in
Ithaca, NY. Allen is a senior member of ASQ.

CHRISTOPHER A. SEAMAN is a doctoral student in
mathematics at the Graduate Center of City University of New
York.